The generator matrix

 1  0  1  1  1 3X+2  1  1 3X  1  1  2  1  1  1  1  1  1  1  1  0 3X+2  2 3X  1  1  1  1 2X  1
 0  1 X+1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 3X+2 X+1 2X+3  2 3X X+3 2X+1  1  1  1  1 2X X+2 2X+2  X  0 2X
 0  0 2X 2X  0 2X 2X  0  0  0 2X 2X 2X  0  0 2X  0 2X 2X  0 2X  0  0 2X 2X  0  0 2X 2X 2X

generates a code of length 30 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+34x^28+268x^29+58x^30+40x^31+29x^32+76x^33+4x^34+2x^42

The gray image is a code over GF(2) with n=240, k=9 and d=112.
This code was found by Heurico 1.16 in 1.05e-007 seconds.